People have been asking for this to change for the last 3 years. So what do the devs do, make it worse for the next DLC with a limited colony rush (6 maybe 7 colony ships max for the first 50 turns).

The AI does not currently do influence, ever. And as the OP pointed out they are settling in such a massive influence zone, even if they did do influence it would be wasted money (rushing, cause they would have too) due to influence requireing time to build and yours been so overpowerign the planets flip within a turn or 2.

I actually use this as a strategy, settle core worlds in good systems leave the other planets, plop a Culture starbase at every system within reasonable range and let the AI burn through its limited Admins colonizing planets in my overpowering Influence zone, saves me atleast 5+ citizens (Since I do no have to worry about colony ships overly much), cheesey, ofc it is, its a mechanic they do not seem to want to fix so its working as intended (you know just like commonwealths).

This tactic has also been pushed into no1 spot for the up comming expansion due to the limited growth rate which in turn limits how much/fast you can colonize (unless they fix the fact AI do not do influence).

They get a flat bonus every time they gain a Ideology perk (Which give them a decent sphere), they do not put sensors or any other influence buffing modules on starbases. Do not build Cultural Starbases or influence improvements unless its a secondary type and the main type gives a different bonus they were after. Its why Influence victory is so cheesy.

EDIT: This is what they get:-

    <Triggers>
      <OnEvent>OnCultureTraitUnlock</OnEvent>
      <Scope>Global</Scope>
      <Target>
        <TargetType>Colony</TargetType>
      </Target>
      <Lifetime>Instant</Lifetime>
      <Modifier>
        <EffectType>InfluencePerTurn</EffectType>
        <Scope>Global</Scope>
        <Target>
          <TargetType>Colony</TargetType>
        </Target>
        <BonusType>Flat</BonusType>
        <Value>100</Value>
      </Modifier>
    </Triggers>

Everytime they unlock an ideology perk, that is the equivelent of 20 Consulate improvements on every single planet, every single time they unlock an Ideology perk, its more of a hack/cheat than an actuall ability tbh. Or an AI that actually specificly uses Influence to win.

What happens if influence is put to the top of their priority list?